Ellipsoidal cyclotron mass ($m_c^2=\det M/({\hat{\mathbf{B}}}^{T}M\hat{\mathbf{B}})$)

For a positive definite parabolic effective mass tensor $M$, the Lorentz force equation is $M\dot{\mathbf{v}}=e\mathbf{B}\times \mathbf{v}$. Its nonzero eigenfrequencies are $\pm eB/m_c$, giving the displayed mass. With principal values $(m_t,m_t,m_l)$, a field along the long valley axis gives $m_c=m_t$; a perpendicular field gives $\sqrt{m_t{m}_l}$. For equally oriented cubic valleys viewed along $[111]$, all valleys give $m_c=\sqrt{3m_t^2{m}_l/(2m_t+m_l)}$.